Quantum theory shortcomings

The theory of solvent effects on standard solutes and on chemically reacting species has been developed in this chapter. Some shortcomings related to the Bom-Oppenheimer view that are important at the interconversion domains have been discussed. A quantum theory of chemical interconversion in the gas-phase and in passive solvent media has been introduced. This is an extention of our earlier ideas [43],... 

Despite its shortcomings, however, the Bohr-Sommerfeld model is of enormous significance in the development of the quantum theory and, in a broader sense, as an illustration of the evolution of scientific ideas. 

It should be stated at the beginning that despite quite numerous partial successes the present state of the quantum-chemical theory of reactivity is far from satisfactory. First of all, it is not clear whether the present shortcomings are due to the non-adequacy of models of activated complexes or to the drastic approximations made in the calculation of the energy of the activated complex and the reactants. On the other hand, some other deficiencies of most of the reported attempts to interpret reactivity in terms of the theory are obvious the very nature of the HMO method is thought148 to make it necessary to treat as large sets of theoretical and experimental data as possible and, in addition, to respect the distinction in properties of the three classes of positions mentioned (in this connection we do not refer to the difference in the stereochemistry of these positions). 

This discussion could be conducted in two ways. First, we could try to deduce structural information from experimental facts through unequivocal mathematical calculations. This would be most satisfying and certainly constitutes the ultimate goal for structural studies. Unfortunately, divergencies of opinions currently observed show that we are still far from such achievement. One important reason for these difficulties may be that quantum mechanical treatment of d orbitals has not reached the precision attained for s and p orbitals. So, in many cases, it cannot be said whether discrepancies between experience and theory are due to inadequacy of theoretical concepts or to shortcomings of mathematical tools. 

It is a remarkable and not yet satisfactorily explained phenomenon that in spite of the apparent shortcomings and suspicious quantum-physical basis of the HMO theory, in some cases its results are in good quantitative agreement with experimental data. In particular, this applies to the total ji-electron energy, especially in the case of benzenoid hydrocarbons. This fortunate feature of the HMO theory is discussed in more detail in the subsequent section. 

Another obvious shortcoming of the theory is its classical nature. The need for quantum mechanics can arise in two ways. First and obvious is the possibility that the transition of interest is affected by tunneling or by nonadiabatic curve-crossing transitions. We have discussed the TST aspects of these phenomena in Sections 14.3.5 and 14.3.6. Less obvious is the fact that, as discussed in Sections 13.4.1 and 13.6, quantum mechanical effects in the vibrational energy relaxation of small molecules can be very large. Both these manifestations of quantum effects in barrier crossing become important, in particular, at low temperatures. 

Analytic gradient and second derivative methods in quantum chemistry provide the type of information about the PES which we need to implement a reaction path approach. Here the major shortcoming is the lack of analytic (relatively inexpensive) gradient and second derivative formulas for highly correlated levels of theory. 

In a certain sense, the question of the reality of atoms was therefore displaced by the question of what constituted a valid chemical explanation in terms of atoms. In the nineteenth century, atomic theory had the shortcoming that it was not furnished with a suitable mechanics, a theory of what went on inside the atom. As Nye (1993) has stated, a mechanical explanation of the behaviour of atoms was the elusive dream of chemistry. Before quantum chemistry, and to a large extent even after its rise, this dream was not relinquished rather, it was repressed (page 71). 

Since transition state theory is derived from a classical flux correlation function, it has all shortcomings of a classical description of the reaction process. Neither tunneling, which is especially important for H-atom transfer processes or low temperature reactions, nor zero point energy effects are included in the description. Thus, the idea to develop a quantum transition state theory (QTST) which accounts for quantum effects but retains the computational advantages of the transition state approximation has been very attractive (for examples see Refs.[5, 6] and references therein). The computation of these QTST rate constants does not require the calculation of real-time dynamics and is therefore feasible for large molecular systems. 

This article provides a comprehensive review of modem approaches to analysis of electronic wavefunctions. Diverse definitions of properties such as atomic charges, energies, and valences, bond orders and energies, specialized orbitals, and similarities of atoms and molecules are presented. The merits and shortcomings of these definitions are discussed, Particular emphasis is placed on rigorous interpretive tools which produce quantities that can be regarded as tme quantum mechanical observables. Because of their lack of generality, approaches to quantification of chemical concepts that are limited to certain classes of molecules or electronic stmcture methods (such as n -electron bond orders in Hiickel theory) are not mentioned. 

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